Shimura Varieties and Trace Formula Seminar

In this lecture, we will try to explain the essential ingredients in the construction of toroidal and minimal compactifications of smooth integral models of (general) PEL-type Shimura varieties, following the approaches of Faltings and Chai. Since this is rather an archaic problem, our goal will be to identify the main difficulties that are absent in the special cases worked out in the literature, and to explain why there could be a uniform solution to such difficulties.